Question

Two firms are competing in prices. Each has two strategies: undercut and cooperate. The firms’ payoffs are provided in the matrix below

Undercut Firm 1

Cooperate

Firm 2
Undercut Cooperate

100, 100	1000, 0
0, 1000	500, 500

(a) (3 points) Assume the firms make their decisions at the same time, and the firms’ competition lasts for one year. Does Firm 1 have a dominant strategy? Does Firm 2 have a dominant strategy? Find the Nash equilibrium.

2

2. (b) (2 points) Suppose Firm 1 moves first. Draw a decision tree and find the Nash equilibrium.

3. (c) (3 points) Is there a first mover advantage? Explain.

4. (d) (3 points) Can the cooperative outcome be achieved if firms know that their

   competition will last for 10 years?

5. (e) (6 points) Suppose the game is infinitely repeated, and the discount rate is r = 0.08. Is cooperation optimal? Explain. What is the lowest discount rate at which cooperation is not optimal?

Answer 1

A).

Consider the given problem here there are two firms “firm1” and “firm2” both of them having two possible strategies “U = Under Cut” and “C = Cooperate”. Now, if “firm1” chooses to undercut then the best possible option for “firm2” is to undercut, because 100 > 0. Similarly, if “firm1” chooses to cooperate then the best possible option for “firm2” is to undercut, because 1000 > 500. So, “undercut” is dominated strategy for “firm2”. Similarly, “undercut” is also dominated strategy for “firm1”.

So, the only NE is “Undercut, Undercut” and both will get payoff “100” respectively.

B).

Let’s assume firm1 moves 1^st then firm2 takes its optimum strategy by observing “firm1” choice.

Here if “firm1” choose to “undercut” then “firm2” will choose undercut and both will get “100” as a payoff. If “firm1” choose to “cooperate” then “firm2” will choose undercut and both will get “0” and “1000” respectively as a payoff.

So, as a rational player “firm1” decide to choose “undercut” and the NE is “undercut, undercut” will get payoff “100, 100”.

C).

Here in this game there don’t have any 1^st mover advantage. Since in the fomer case and in the latter case the NE are same. So, there don’t have any 1^st mover advantage.

D).

If the same game is player for 10 years then also cooperation will not possible. Since in the last period both will cheat by choosing “undercut” to maximize their payoff. So, both will continue to “undercut” form the 1^st period. So, the cooperation is not possible if the game is played for a finite numbers of periods.